Modification of a fraction involving logarithms | Mathematics | Page 1

glacial marlin Oct 12, 2024, 8:20 PM

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I'm trying to find a convergent series for which Raabe's ratio test yields 1. I've been able to find only one example, that being the series a_n = 1/n*log^2(n). However, I struggle modifying the a_n+1/a_n fraction into something workable. On https://math.stackexchange.com/questions/4446815/example-where-raabes-test-is-inconclusive they got the result in the pic, but I don't seem to understand what operations they did. Alternatively, a simpler convergent series which yields 1 in Raabe's test would also be helpful.

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Example where Raabe's Test is inconclusive

I was looking for an example of a convergent series for which the Raabe's test is inconclusive. I found the series $\sum_{n=2}^{\infty}\frac{1}{n\operatorname{log}^2n}$, which can easily be shown t...

wind jettyBOT Oct 12, 2024, 8:20 PM

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glacial marlin Oct 12, 2024, 8:21 PM

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I understand how they got (1+1/n), but the rest is a mystery to me.

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Seems like there are identities I was unaware of.

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I tried applying it and got the same result.

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.solved

#Modification of a fraction involving logarithms